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New edge states discovered in photonic graphene


An artificial graphene reveals new undiscovered properties.

Following the discovery of graphene and its remarkable electronic properties, a new field of research, that of “artificial graphenes”, has been developed. Its aim is to study and to transfer the properties of graphene to other physical systems. In that manner, honeycomb lattices consisting of microwave resonators or lattices of cold atoms, trapped in optical potentials, have allowed to probe physical properties inaccessible in electronic graphene [1].

In addition, “artificial graphenes” unveil new physical properties that are not present in the two-dimensional carbon sheet. This is the case of honeycomb lattices of microcavity polaritons. Polaritons are mixed light-matter quasiparticles that arise from the strong coupling between electronic excitations (so called excitons) and photons confined in a cavity (fig 1(a)). One such cavity, shaped in the form of a micropillar with lateral dimensions on the order of few microns, behaves like an artificial atom : its discrete energy states (orbitals) are the allowed modes of confined photons (fig 1(b)).

Fig 1 : (a) Polaritons in a micropillar : Light is confined in a GaAs cavity (green) where it interacts with quantum well excitons (red). (b) Photonic states are discrete, like the electronic levels in an atom. (c) Honeycomb lattice of overlapping pillars. Polaritons can propagate in this lattice, like electrons do in graphene. (d) Orbital graphene is obtained by coupling the px and py states of adjacent sites in the lattice. (e) The band structure has two additional bands (yellow and red) with respect to that of graphene.

As these cavities are coupled to make a honeycomb lattice (fig 1(c)), they form an artificial structure analogue to graphene : the micropillars play the role of carbon atoms, and polaritons, which propagate between the pillars, play the role of electrons. One of the advantages of this system is the possibility to probe the higher orbitals of the pillars, that is, the higher energy bands of graphene (fig 1(d)). These are inaccessible in graphene due to hybridization of the bands. The high energy orbitals form 4 bands with a remarkable structure : two dispersive bands which intersect in the Dirac cones (like in graphene), sandwiched in between two additional bands that are flat (fig 1(e)).

The work, result of a collaboration between C2N in Marcoussis on the experimental side, and LPS and BEC-Center of Department of Physics of University of Trento for the theory, consisted in the direct observation and characterization of edge states associated with these new bands (fig. 2). Remarkably, new flat zero energy edge states were discovered, whose position in momentum space is complementary to the ones of graphene. Additionally, new edge states with dispersive character, and thus suitable for carrying transport, were found for all types of terminations including armchair, which doesn’t show any edge states in the case of graphene.

The importance of this work is the demonstration of novel types of edge states in honeycomb lattices. When including polariton-polariton interactions or adding an external magnetic field, we expect the emergence of new exotic phenomena proper to synthetic matter.

Fig. 2 (a) Optical microscope image of a two dimensional polariton honeycomb lattice with the three types of edges. (b) Dispersion relation in the bulk measured in a luminescence experiment. (c) at the edges new edge states appear (dashed ellipses). (d) Bulk states (blue) and edge states (red) obtained by tight binding calculation in the nearest neighbour approximation.

[1] For more details see the news of CNRS from 23rd May 2012 : Using cold atoms to understand dynamics of electrons in graphene and that of 5th February 2013 : Exploring topological phase transition equivalent to that one in graphene using microwaves

Reference

Orbital Edge States in a Photonic Honeycomb Lattice
M. Milićević, T. Ozawa, G. Montambaux, I. Carusotto, E. Galopin, A. Lemaître, L. Le Gratiet, I. Sagnes, J. Bloch, and A. Amo
Physical Review Letters 118, 107403 (2017)
doi:10.1103/PhysRevLett.118.107403

Contact

Gilles Montambaux, Jacqueline Bloch, Alberto Amo